Pedagogical Enhancements To The Desymbol Logic Translator,
2013
Rowan University
Pedagogical Enhancements To The Desymbol Logic Translator, Darren F. Provine, Nancy Lynn Tinkham
ACMS Conference Proceedings 2013
DeSymbol is a program that translates first-order predicate logic expressions into English. It is intended to be a practice tool for students who are learning logic for the first time or who are trying to refresh their memories if they need to use symbolic logic for an upper-level course. Students start with an English sentence and translate it by hand into symbolic logic notation; then they can check their work by using DeSymbol to translate their notation back into English. If the English sentence produced by DeSymbol differs significantly from the original English sentence, this helps the student to see …
Mapping Biblical Commandments To An Iterated Prisoner’S Dilemma Framework,
2013
Bethel University
Mapping Biblical Commandments To An Iterated Prisoner’S Dilemma Framework, Nathan Gossett, Adam Johnson
ACMS Conference Proceedings 2013
In his writings on Game Theory, an d the Iterated Prisoner’s Dilemma in particular, Robert Axelrod outlined four properties that are predictors of a successful strategy: Niceness, Reciprocity, Forgiveness, and Understandability. On the topic of Reciprocity, Axelrod makes the claim that not only does The Golden Rule lead to a suboptimal strategy, but that one of the most successful strategies (Tit for Tat) shows that a command of “An eye for an eye” leads to a much more optimal strategy. In this paper, we will discuss the details of Axelrod’s four properties, outline Biblical support for all four, and discuss …
Open Source Software: What Is It, And Why Should We Care?,
2013
Gordon College
Open Source Software: What Is It, And Why Should We Care?, Karl-Dieter Crisman
ACMS Conference Proceedings 2013
This paper examines the distinctions in talking about computer software that has implications for both mathematics and moral thought.
Teaching Complex Analysis As A Lab-Type Course With A Focus On Geometric Interpretations Using Mathematics,
2013
Taylor University
Teaching Complex Analysis As A Lab-Type Course With A Focus On Geometric Interpretations Using Mathematics, William M. Kinney
ACMS Conference Proceedings 2013
I taught complex analysis for the first time in my career during the spring of 2013. I decided to do something “radical” and teach it as a lab-type course with a focus on geometric interpretations using the computer program Mathematica. The students and I met in a computer lab and, during most meetings, we spent a large portion of our time experimenting and exploring using Mathematica to visualize key concepts in complex analysis. Because of this, there was a heavy emphasis on viewing analytic functions as conformal mappings as well as considering associated vector fields and flows. Mathematica was used …
Faith Integration Projects For First-Year Students,
2013
Messiah College
Faith Integration Projects For First-Year Students, Doug Phillippy
ACMS Conference Proceedings 2013
This talk will consider the use of projects to motivate students to think deeply about how their faith connects with mathematics. This talk will begin by describing what a faith integration project is, including the goals and objectives of such a project. The talk will briefly describe a number of projects written by the speaker, with a more detailed look at one of those projects. The talk will conclude by discussing how these projects are being used to assess how students are doing at articulating a maturing understanding of the connection between faith and mathematics
Philosophy Motivates Undergraduates In Mathematics,
2013
Highland Community College
Philosophy Motivates Undergraduates In Mathematics, Dustin Wilson
ACMS Conference Proceedings 2013
A talk on how elective seminars on the philosophy of mathematics can inspire undergraduate students to pursue and persist in mathematics.
Forming The Analytical Society At Cambridge University,
2013
Gordon College
Forming The Analytical Society At Cambridge University, Richard Stout
ACMS Conference Proceedings 2013
The Analytical Society, an organization begun by students at Cambridge, was founded in 1812. Even though it was entirely student-led, the society was responsible for significant changes in the Cambridge mathematics curriculum and in the way mathematics was perceived in Britain throughout the nineteenth century. Its success was likely due to the outstanding students who formed the group, some of whom went on to become leaders in British science and mathematics for the next fifty years. In this paper we will briefly look at several of those who played important roles in forming and leading the society and we will …
The Unity Of Knowledge And The Faithfulness Of God: The Theology Of Mathematical Physicist John Polkinghorne,
2013
Marian University - Indianapolis
The Unity Of Knowledge And The Faithfulness Of God: The Theology Of Mathematical Physicist John Polkinghorne, Matt Delong
ACMS Conference Proceedings 2013
In this paper we will give a brief introduction to Polkinghorne's life and work. We will give an introduction to Polkinghorne's approach to philosophy and theology. We will introduce the two most significant influences on Polkinghorne's development as a theologian and philosopher of science. We will then give a necessarily telegraphic review of some of the topics addressed in Polkinghorne's theology, including his thoughts on science and religion, natural theology, evil, providence, prayer, resurrection, the soul and eschatology. We will then conclude with a few short examples of Polkinghorne's thoughts on mathematics.
Leading A Successful Missions Trip In Your Discipline,
2013
Taylor University
Leading A Successful Missions Trip In Your Discipline, Tom Nurkkala, Darci Nurkkala
ACMS Conference Proceedings 2013
The global missions community goes wanting for skilled workers in almost every discipline. However, even students at a Christian institution that emphasizes global engagement remain largely unaware of the impact they can make in missions by leveraging their own academic specialty. In this paper, we draw on our experience leading discipline-specific missions trips as a means to encourage students to reframe their thinking about personal involvement in missions. We discuss the need for students to experience missions firsthand, and the student outcomes we have observed in intercultural awareness and spiritual formation. A key student outcome is an increased willingness to …
Googol-Part Fugue: Another Imagination Of Divine Providence And Game Theory,
2013
NumberSciences
Googol-Part Fugue: Another Imagination Of Divine Providence And Game Theory, Gideon Lee
ACMS Conference Proceedings 2013
The problem of evil presents an intellectual hurdle for some to believe in a good and omnipotent God. The emergence of open theism could be seen as an attempt to make a stronger case for the free will defense. However, in denying divine foreknowledge as traditionally understood, open theism contradicts biblical revelation not only in its direct claims, but also when its logical implications for divine providence are worked out. The open theist Alan Rhoda has sought to explain through game theory how some degree of divine providence is possible under open theism. That explanation is astonishing since the open …
Life Lessons From Leibniz,
2013
King University
Life Lessons From Leibniz, Andrew J. Simoson
ACMS Conference Proceedings 2013
The tri-centennial of Leibniz’s death is nigh (2016). And 2013 is not too early to begin a special celebration of this man of mathematics. Besides being the co-discoverer of calculus and the implementer of binary numbers, formal logic, and formal languages, all of which foreshadowed the computer age, Leibniz is said to be one of the last to know almost everything that was known about almost anything. Professionally, his occupation was librarian in the princely court of Hanover in oldGermany. Serving under three different princes, the last of whom became George I of England, Leibniz had to continual lyre-invent himself—somewhat …
Al-Khwārizmī: Founder Of Classical Algebra,
2013
Dordt College
Al-Khwārizmī: Founder Of Classical Algebra, Calvin Jongsma
ACMS Conference Proceedings 2013
Adopting a historically defensible definition of “algebra,” we will begin by exploring a few examples of algebra prior toal-Khwarizmi. We will then examine what algebra became through al-Khwarizmi’s work. In conclusion, we will assess thehistorical importance of al-Khwarizmi’s contributions for developments in European algebra.
Expanding Jonathan Edwards’ Typology Program: The Bell Curve As A Type Of Christ,
2013
Biola University
Expanding Jonathan Edwards’ Typology Program: The Bell Curve As A Type Of Christ, Jason Wilson
ACMS Conference Proceedings 2013
Over two hundred years after his death, an unfinished notebook of Jonathan Edwards’ was published for the first time in1993. Edwards was a father of the Evangelical movement, but because his work on typology was not published until recently, it has received almost no attention. In his notebook, Edwards makes an explicit argument for extending biblical typology to nature in a biblically grounded manner. This study is an attempt to extend that research program into mathematics/statistics.We will consider the following proposition, “The normal distribution (the graph of which is the bell curve) is a biblical type of Christ.” The basic …
Delaware, Dickeson, Assessment And How You Can Help,
2013
Point Loma Nazarene University
Delaware, Dickeson, Assessment And How You Can Help, Greg Crow, Maria Zack
ACMS Conference Proceedings 2013
How much release time should a chair receive? What is the cost per unit for a particular academic program? What is a student credit hour (SCH) anyway and why would anyone care? Why are so many boards enamored of Delaware, Dickeson and Assessment? The answer to these and many related questions will be presented in this talk. Analytics and various“efficiency measures” are becoming increasingly important in higher education and mathematicians and computer scientists are being regularly recruited to help university administrators make meaning from large volumes of data. Come and learn about this trend and how you can be of …
An Ε -Uniform Numerical Method For A System Of Convection-Diffusion Equations With Discontinuous Convection Coefficients And Source Terms,
2013
Bharathidasan University College
An Ε -Uniform Numerical Method For A System Of Convection-Diffusion Equations With Discontinuous Convection Coefficients And Source Terms, T. Valanarasu, R. M. Priyadharshini, N. Ramanujam, A. Tamilselvan
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, a parameter-uniform numerical method is suggested to solve a system of singularly perturbed convection-diffusion equations with discontinuous convection coefficients and source terms subject to the Dirichlet boundary condition. The second derivative of each equation is multiplied by a distinctly small parameter, which leads to an overlap and interacting interior layer. A numerical method based on a piecewise uniform Shishkin mesh is constructed. Numerical results are presented to support the theoretical results.
Solutions Of System Of Fractional Partial Differential Equations,
2013
Bharathiar University
Solutions Of System Of Fractional Partial Differential Equations, V. Parthiban, K. Balachandran
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, system of fractional partial differential equation which has numerous applications in many fields of science is considered. Adomian decomposition method, a novel method is used to solve these type of equations. The solutions are derived in convergent series form which shows the effectiveness of the method for solving wide variety of fractional differential equations.
Solving Singularly Perturbed Differential Difference Equations Via Fitted Method,
2013
Bahir Dar University
Solving Singularly Perturbed Differential Difference Equations Via Fitted Method, Awoke Andargie, Y. N. Reddy
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we presented a fitted approach to solve singularly perturbed differential difference equations of second order with boundary at one end (left or right) of the interval. In this approach, with the help of Taylor series expansion, we approximated the terms containing negative and positive shifts and modified the singularly perturbed differential difference equation to singularly perturbed differential equation. A fitting parameter in the coefficient of the highest order derivative of the new equation is introduced and determined its value from the theory of singular perturbation. Finally, we obtained a three term recurrence relation which is solved using …
Physically-Realizable Uniform Temperature Boundary Condition Specification On A Wall Of An Enclosure: Part I – Problem Investigation,
2013
Kutztown University of Pennsylvania
Physically-Realizable Uniform Temperature Boundary Condition Specification On A Wall Of An Enclosure: Part I – Problem Investigation, P. Y. C. Lee, W. H. Leong
Applications and Applied Mathematics: An International Journal (AAM)
Designing an experimental apparatus requires considerable amount of planning. Despite proper planning, one can easily overlook a design such as the standard uniform temperature boundary condition applied to all or portion of a wall of an experimental apparatus. Although this boundary condition is mathematically simple and precise, achieving it physically may not be that simple. This paper addresses one such three-dimensional natural convection heat transfer apparatus that was designed to measure benchmark Nusselt numbers at various Rayleigh numbers with uniform temperatures specified at two walls of the enclosure. It was found that the effect of thermal spreading/constriction resistance on one …
Projected Surface Finite Elements For Elliptic Equations,
2013
University of Tulsa
Projected Surface Finite Elements For Elliptic Equations, Necibe Tuncer
Applications and Applied Mathematics: An International Journal (AAM)
In this article, we define a new finite element method for numerically approximating solutions of elliptic partial differential equations defined on “arbitrary” smooth surfaces S in RN+1. By “arbitrary” smooth surfaces, we mean surfaces that can be implicitly represented as level sets of smooth functions. The key idea is to first approximate the surface S by a polyhedral surface Sh, which is a union of planar triangles whose vertices lie on S; then to project Sh onto S. With this method, we can also approximate the eigenvalues and eigenfunctions of th Laplace-Beltrami operator on these “arbitrary” surfaces.
Physically-Realizable Uniform Temperature Boundary Condition Specification On A Wall Of An Enclosure: Part Ii – Problem Solution,
2013
Kutztown University of Pennsylvania
Physically-Realizable Uniform Temperature Boundary Condition Specification On A Wall Of An Enclosure: Part Ii – Problem Solution, P. Y. C. Lee, W. H. Leong
Applications and Applied Mathematics: An International Journal (AAM)
Temperature measurements along one side of the rectangular plate showed severe temperature non-uniformity along one side of a wall of a cubical experimental apparatus where the uniform temperature was physically desired. Despite proper planning and analyses, this non-uniformity was high enough that a benchmark study could not be carried out to the desired accuracy of about one percent error. This paper presents and extends analyses made previously based on the modifications to the original design of the apparatus to reduce the temperature non-uniformity on the wall by adding an auxiliary heater around a wall where the uniform temperature was desired. …
